Oscillation - Real-life applications

Photo by: chrisharvey

Springs and Damping

Elastic potential energy relates primarily to springs, but springs are
a major part of everyday life. They can be found in everything from
the shock-absorber assembly of a motor vehicle to the supports of a
trampoline fabric, and in both cases, springs blunt the force of
impact.

If one were to jump on a piece of trampoline fabric stretched across
an ordinary table—one with no springs—the experience
would not be much fun, because there would be little bounce. On the
other hand, the elastic potential energy of the trampoline's
springs ensures that anyone of normal weight who jumps on the
trampoline is liable to bounce some distance into the air. As a
person's body comes down onto the trampoline fabric, this
stretches the fabric (itself highly elastic) and, hence, the springs.
Pulled from a position of equilibrium, the springs acquire elastic
potential energy, and this energy makes possible the upward bounce.

As a car goes over a bump, the spring in its shock-absorber assembly
is compressed, but the elastic potential energy of the spring
immediately forces it back to a position of equilibrium, thus ensuring
that the bump is not felt throughout the entire vehicle. However,
springs alone would make for a bouncy ride; hence, a modern vehicle
also has shock absorbers. The shock absorber, a cylinder in which a
piston pushes down on a quantity of oil, acts as a damper—that
is, an inhibitor of the springs' oscillation.

SIMPLE HARMONIC MOTION AND DAMPING.

Simple harmonic motion occurs when a particle or object moves back and
forth within a stable equilibrium position under the influence of a
restoring force proportional to its displacement. In an ideal
situation, where friction played no part, an object would continue to
oscillate indefinitely.

Of course, objects in the real world do not experience perpetual
oscillation; instead, most oscillating particles are subject to
damping, or the dissipation of energy, primarily as a result of
friction. In the earlier illustration of the spring suspended from a
ceiling, if the string is pulled to a position of maximum displacement
and then released, it will, of course, behave dramatically at first.
Over time, however, its movements will become slower and slower,
because of the damping effect of frictional forces.

HOW DAMPING WORKS.

When the spring is first released, most likely it will fly upward with
so much kinetic energy that it will, quite literally, bounce off the
ceiling. But with each transit within the position of equilibrium, the
friction produced by contact between the metal spring and the air, and
by contact between molecules within the spring itself, will gradually
reduce the energy that gives it movement. In time, it will come to a
stop.

If the damping effect is small, the amplitude will gradually decrease,
as the object continues to oscillate, until eventually oscillation
ceases. On the other hand, the object may be
"overdamped," such that it completes only a few cycles
before ceasing to oscillate altogether. In the spring illustration,
overdamping would occur if one were to grab the spring on a downward
cycle, then slowly let it go, such that it no longer bounced.

There is a type of damping less forceful than overdamping, but not so
gradual as the slow dissipation of energy due to frictional forces
alone. This is called critical damping. In a critically damped
oscillator, the oscillating material is made to return to equilibrium
as quickly as possible without oscillating. An example of a critically
damped oscillator is the shock-absorber assembly described earlier.

Even without its shock absorbers, the springs in a car would be
subject to some degree of damping that would eventually bring a halt
to their oscillation; but because this damping is of a very gradual
nature, their tendency is to continue oscillating more or less evenly.
Over time, of course, the friction in the springs would wear down
their energy and bring an end to their oscillation, but by then, the
car would most likely have hit another bump. Therefore, it makes sense
to apply critical damping to the oscillation of the springs by using
shock absorbers.

Bungee Cords and Rubber Bands

Many objects in daily life oscillate in a spring-like way, yet people
do not commonly associate them with springs. For example, a rubber
band, which behaves very much like a spring, possesses high elastic
potential energy. It will oscillate when stretched from a position of
stable equilibrium.

Rubber is composed of long, thin molecules called polymers, which are
arranged side by side. The chemical bonds between the atoms in a
polymer are flexible and tend to rotate, producing kinks and loops
along the length of the molecule. The super-elastic polymers in rubber
are called elastomers, and when a piece of rubber is pulled, the kinks
and loops in the elastomers straighten.

The structure of rubber gives it a high degree of elastic potential
energy, and in order to stretch rubber to maximum displacement, there
is a powerful restoring force that must be overcome. This can be
illustrated if a rubber band is attached to a ceiling, like the spring
in the earlier example, and allowed to hang downward. If it is pulled
down and released, it will behave much as the spring did.

The oscillation of a rubber band will be even more appreciable if a
weight is attached to the "free" end—that is, the
end hanging downward. This is equivalent, on a small scale, to a
bungee jumper attached to a cord. The type of cord used for bungee
jumping is highly elastic; otherwise, the sport would be even more
dangerous than it already is. Because of the cord's elasticity,
when the bungee jumper "reaches the end of his rope," he
bounces back up. At a certain point, he begins to fall again, then
bounces back up, and so on, oscillating until he reaches the point of
stable equilibrium.

The Pendulum

As noted earlier, a pendulum operates in much the same way as a swing;
the difference between them is primarily one of purpose. A swing
exists to give pleasure to a child, or a certain bittersweet pleasure
to an adult reliving a childhood experience. A pendulum, on the other
hand, is not for play; it performs the function of providing a
reading, or measurement.

One type of pendulum is a metronome, which registers the tempo or
speed of music. Housed in a hollow box shaped like a pyramid, a
metronome consists of a pendulum attached to a sliding weight, with a
fixed weight attached to the bottom end of the pendulum. It includes a
number scale indicating the number of oscillations per minute, and by
moving the upper weight, one can change the beat to be indicated.

ZHANG HENG'S SEISMO-SCOPE.

Metronomes were developed in the early nineteenth century, but, by
then, the concept of a pendulum was already old. In the second century
A.D.
, Chinese mathematician and astronomer Zhang Heng (78-139) used a
pendulum to develop the world's first seismoscope, an
instrument for measuring motion on Earth's surface as a result
of earthquakes.

Zhang Heng's seismoscope, which he unveiled in 132
A.D.
, consisted of a cylinder surrounded by bronze dragons with frogs
(also made of bronze) beneath. When the earth shook, a ball would drop
from a dragon's mouth into that of a frog, making a noise. The
number of balls released, and the direction in which they fell,
indicated the magnitude and location of the seismic disruption.

CLOCKS, SCIENTIFIC INSTRUMENTS, AND "FAX MACHINE".

In 718
A.D.
, during a period of intellectual flowering that attended the early
T'ang Dynasty (618-907), a Buddhist monk named I-hsing and a
military engineer named Liang Ling-tsan built an astronomical clock
using a pendulum. Many clocks today—for example, the stately
and imposing "grandfather clock" found in some
homes—like-wise, use a pendulum to mark time.

Physicists of the early modern era used pendula (the plural of
pendulum) for a number of interesting purposes, including calculations
regarding gravitational force. Experiments with pendula by Galileo
Galilei (1564-1642) led to the creation of the mechanical pendulum
clock—the grandfather clock, that is—by distinguished
Dutch physicist and astronomer Christiaan Huygens (1629-1695).

In the nineteenth century, A Scottish inventor named Alexander Bain
(1810-1877) even used a pendulum to create the first "fax
machine." Using matching pendulum transmitters and receivers
that sent and received electrical impulses, he created a crude device
that, at the time, seemed to have little practical purpose. In fact,
Bain's "fax machine," invented in 1840, was more
than a century ahead of its time.

THE FOUCAULT PENDULUM.

By far the most important experiments with pendula during the
nineteenth century, however, were those of the French physicist Jean
Bernard Leon Foucault (1819-1868). Swinging a heavy iron ball from a
wire more than 200 ft (61 m) in length, he was able to demonstrate
that Earth rotates on its axis.

Foucault conducted his famous demonstration in the Panthéon, a
large domed building in Paris named after the ancient Pantheon of
Rome. He arranged to have sand placed on the floor of the
Panthéon, and placed a pin on the bottom of the iron ball, so
that it would mark the sand as the pendulum moved. A pendulum in
oscillation maintains its orientation, yet the Foucault pendulum (as
it came to be called) seemed to be shifting continually toward the
right, as indicated by the marks in the sand.

The confusion related to reference point: since Earth's
rotation is not something that can be perceived with the senses, it
was natural to assume that the pendulum itself was changing
orientation—or rather, that only the pendulum was moving. In
fact, the path of Foucault's pendulum did not vary nearly as
much as it seemed. Earth itself was moving beneath the pendulum,
providing an additional force which caused the pendulum's plane
of oscillation to rotate.